title: Universal fractional map and cascade of bifurcations type attractors.
abstract: We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α>0, which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We consider two particular α-families corresponding to the Standard and Logistic Maps. For fractional α<2 in the area of parameter values of the transition through the period doubling cascade of bifurcations from regular to chaotic motion in regular dynamics corresponding fractional systems demonstrate a new type of attractors--cascade of bifurcations type trajectories.
authors.affiliation: Department of Physics, Stern College at Yeshiva University, 245 Lexington Ave, New York, New York 10016, USA and Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA.
authors.forename: M
authors.initials: M
authors.lastname: Edelman
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods; D003198:Computer Simulation; D004574:Electromagnetic Fields; D006801:Humans; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D014783:Viscosity